Lindsey Graham takes on Clinton, Trump over immigration

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Photos:Lindsey Graham's political career

Click through to see highlights from U.S. Sen. Lindsey Graham's political career:

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Photos:Lindsey Graham's political career

Graham; Sir Elton John, center; and filmmaker and John's husband, David Furnish, pose after testimony at a U.S. Senate hearing on the global fight against AIDS on May 6, 2015. Graham and Democratic Sen. Patrick J. Leahy of Vermont hosted John as part of their bipartisan effort to combat HIV infection.

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Photos:Lindsey Graham's political career

Graham rushes to the Senate chamber to vote on an attempt to override U.S. President Barack Obama's veto of the Keystone XL Pipeline legislation March 4, 2015. Graham was elected to the U.S. Senate in 2002 and was re-elected in 2008 and 2014.

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Photos:Lindsey Graham's political career

Graham listens to testimony during a Senate Armed Services Committee meeting on national security strategy on January 27, 2015. According to his website, Graham continues to serve his country in the U.S. Air Force Reserves as a senior individual mobilization augmentee to the judge advocate general.

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Photos:Lindsey Graham's political career

Graham arrives for a closed briefing of the Armed Services Committee on July 30, 2014. Before serving in the Senate, Graham was elected to the U.S. House of Representatives in 1994.

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Photos:Lindsey Graham's political career

Graham talks to U.S. Sen. Marco Rubio, R-Florida, before a news conference on Capitol Hill on July 24, 2014.

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Photos:Lindsey Graham's political career

Graham and U.S. Sen. Ted Cruz, R-Texas, right, listen as President Barack Obama delivers the State of the Union address on January 28, 2014. Graham was in the U.S. Air Force and logged six-and-a-half years of service on active duty as an Air Force lawyer.

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Photos:Lindsey Graham's political career

Graham holds a news conference on Benghazi, Libya, at the U.S. Capitol on October 30, 2013. From left, he is flanked by Sen. John McCain, R-Arizona; Rep. Jason Chaffetz, R-Utah; and Rep. Jim Jordan, R-Ohio. Graham has been an outspoken critic of how the Obama administration has handled the September 11, 2012, attack on the U.S. diplomatic, in which four U.S. citizens died.

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Photos:Lindsey Graham's political career

Israeli Prime Minister Benjamin Netanyahu, center, meets with U.S. Sen. John McCain, R-Arizona, and Graham on June 30, 2013, in Jerusalem.

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Photos:Lindsey Graham's political career

McCain, left, and Graham speak during a news conference about Benghazi on February 14, 2013, on Capitol Hill.

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Photos:Lindsey Graham's political career

Graham talks with reporters before heading into the Senate Republican Caucus policy luncheon at the U.S. Capitol May 8, 2012.

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Photos:Lindsey Graham's political career

Graham speaks to reporters after a news conference about his Social Security reform plan at the U.S. Capitol on April 13, 2011.

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Photos:Lindsey Graham's political career

Graham, left, and McCain call on participants during a health care town hall meeting on September 14, 2009 at the Citadel in Charleston, South Carolina. According to his website, Graham is a native South Carolinian and grew up in a blue collar family in the small town of Central, where his parents ran a restaurant and pool hall.

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U.S. President George W. Bush, left, stands with Graham on the steps of Air Force One at the airport in Greenville, South Carolina, in March 2002.

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Story highlights

Graham's comments come in the wake of national backlash against Trump's remarks about Mexican immigrants, and criticism of the GOP field from Clinton on Tuesday

"My party is in a hole with Hispanics. The first rule of politics when you're in a hole is stop digging. And somebody needs to take a shovel out of Donald Trump's hand," Graham says

Washington (CNN)A defiant Lindsey Graham on Wednesday took on his fellow presidential contenders Hillary Clinton and Donald Trump over immigration.

The South Carolina Republican senator's comments come in the wake of national backlash against Trump's remarks about Mexican immigrants, in which he's called some of them "rapists" and "killers," and criticism from Clinton on Tuesday in which she said none of the Republican presidential candidates support a pathway to citizenship for undocumented immigrants.

But Graham told CNN at the Atlantic Council, a Washington-based think tank focused on international affairs, that when then-Sen. Barack Obama campaigned in 2008, he promised to pass comprehensive immigration reform if elected.

"I want to remind everybody who cares about immigration reform that Obamacare, Dodd-Frank and the stimulus went ahead of you, that he had a chance to transform the system," Graham said. "He didn't lift a finger, nor did she. So I don't need a lecture from Hillary Clinton about immigration reform."

Recalling his participation in various bipartisan "gangs" that worked on immigration reform -- "I've been in every gang you can be in in the Senate. If we had tattoos, I'd have an armful," Graham quipped -- he said he didn't recall Clinton being a part of the discussions.

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"I don't remember seeing her once," Graham said. "I don't remember seeing her at the table. She never came to any of the meetings I was at. She was a public voice in 2009. I never remember her saying, 'wait a minute, President Obama, you promised to do immigration reform, honor your promise.' She didn't say a word."

As for the GOP, Graham said, "My party is in a hole with Hispanics. The first rule of politics when you're in a hole is stop digging. And somebody needs to take a shovel out of Donald Trump's hand."

"I don't need a lecture from Donald Trump or anybody else about border security," Graham added. "Every bill I've ever supported would deport felons on day one. ... The system is completely broken ... but let me tell you how you fix it: Stop talking about it and get Democrats and Republicans to work together."

As for Trump, Graham said: "Here's the mistake. You're right to point out a broken immigration system, but you're wrong to say the following: That of the 11-plus million illegal immigrants, most of them are rapists and drug dealers. Most of them are good, hardworking people, cleaning our toilets, picking the crops that we all enjoy, changing the beds and working three or four jobs in the shadows to try to keep their family afloat. Most of them have come since 1986," he said, a reference to a bill signed into law by President Ronald Reagan that addressed illegal immigration.

Growing emotional as he discussed his personal story, Graham said criminals are not welcome to the U.S., but that he understands the need to keep families together.

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"As to the 11 million, I am telling you as publicly as I know how to tell you, the overwhelming majority of you are here because you left a bad place to find a better place," Graham said. "You've broken our laws and you need to get right, but I see value in you as a human being and we'll try to find a way to fix this without destroying your family. When I was 21, my mom died. When I was 22, my dad died. My sister was 13. If it wasn't for family, friends and faith, I would not be sitting here. I am not going to engage in rhetoric or policies to destroy a family that's done nothing more than try to get a better life for my political gain."

Graham then assailed Trump's rhetoric.

"When it comes to casting a shadow over all of these people, to put them in the group of being rapists and drug dealers, not only is it wrong, you're dealing -- you're digging a bigger hole," he said. "And I hope every Republican candidate would say the following: We disagree with Donald Trump in this regard, that most of the people here illegally are good, hardworking people. And if we're not willing to say that as a party, we're going to lose in 2016."